Deniz S.2024-07-222024-07-22201700221481http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/15296In this paper, the new optimal perturbation iteration method (OPIM) is introduced and applied for solving nonlinear differential equations arising in heat transfer. The effectiveness of the proposed method will be tested by considering two specific applications: the temperature distribution equation in a thick rectangular fin radiation to free space and cooling of a lumped system with variable specific heat. Comparing different methods shows that the results obtained by optimal perturbation iteration method are very good agreement with the numerical solutions and perform better than the most existing analytic methods. Copyright © 2017 by ASME.EnglishDifferential equationsHeat transferIterative methodsNonlinear equationsNumerical methodsSpecific heatAnalytic methodIteration methodNonlinear differential equationNonlinear heat transferNumerical solutionOptimal perturbationPerturbation methodVariable specific-heatPerturbation techniquesArticle10.1115/1.4036085